The impact of aerosols on ice- and mixed-phase processes in deep convective
clouds remains highly uncertain, and the wide range of interacting
microphysical processes is still poorly understood. To understand these
processes, we analyse diagnostic output of all individual microphysical
process rates for two bulk microphysics schemes in the Weather and Research
Forecasting model (WRF). We investigate the response of individual processes
to changes in aerosol conditions and the propagation of perturbations through
the microphysics all the way to the macrophysical development of the
convective clouds. We perform simulations for two different cases of
idealised supercells using two double-moment bulk microphysics
schemes and a bin microphysics scheme. The simulations cover a comprehensive
range of values for cloud droplet number concentration (CDNC) and cloud
condensation nuclei (CCN) concentration as a proxy for aerosol effects on
convective clouds. We have developed a new cloud tracking algorithm to
analyse the morphology and time evolution of individually tracked convective
cells in the simulations and their response to the aerosol perturbations.

This analysis confirms an expected decrease in warm rain formation processes
due to autoconversion and accretion for more polluted conditions. There is no
evidence of a significant increase in the total amount of latent heat, as
changes to the individual components of the integrated latent heating in the
cloud compensate each other. The latent heating from freezing and riming
processes is shifted to a higher altitude in the cloud, but there is no
significant change to the integrated latent heat from freezing. Different
choices in the treatment of deposition and sublimation processes between the
microphysics schemes lead to strong differences including feedbacks onto
condensation and evaporation. These changes in the microphysical processes
explain some of the response in cloud mass and the altitude of the cloud
centre of gravity. However, there remain some contrasts in the development of
the bulk cloud parameters between the microphysics schemes and the two
simulated cases.

Deep convective clouds are an important feature of the Earth's atmosphere,
ranging from widespread convection dominating the atmosphere in the tropics
to mid-latitude convective systems (Emanuel, 1994). The impact
of aerosols on ice- and mixed-phase processes in convective clouds remains
highly uncertain (Tao et al., 2012; Varble, 2018), which has
implications for determining the role of aerosol–cloud interactions in the
climate system. Representing these effects in global climate models poses
additional challenges due to the relatively small length scales often less
than a few kilometres at which convective clouds develop and because of
limitations in the representations of microphysical processes in the
convective parameterisations
(Tao et al., 2012; Boucher et al., 2013; Sullivan et al., 2016), with only few
models explicitly representing the effects of aerosols on deep convective
clouds
(e.g. Song and Zhang, 2011; Guo et al., 2015; Kipling et al., 2017; Zhang et al., 2017; Labbouz et al., 2018).
The highly localised nature of convective processes also leads to major
challenges in observations both from satellites and aircraft measurements
(Rosenfeld et al., 2014).

Over recent years numerous studies using cloud-resolving model simulations
(CRM) have investigated aerosol–convection interactions in various set-ups,
ranging from case study simulations to idealised simulations of squall lines
or supercells like the cases used in this study
(Seifert and Beheng, 2006; Storer et al., 2010; Morrison, 2012; Kalina et al., 2014).
The results, however, vary strongly between many of these studies. The
differences can be attributed to the simulation of different types of
convection or different environmental conditions like humidity or wind shear,
but are also related to differences between the models or modelling
approaches used (Tao et al., 2012; Fan et al., 2016; White et al., 2017).
These challenges in modelling are strongly related to numerous interacting
physical processes (Fan et al., 2016) in cloud microphysics and to the
interaction between clouds and other processes in the atmosphere on different
scales (Tao et al., 2012). In addition to the analysis of process rates in
numerical simulations, analytical evaluations of the microphysical rate
equations of the microphysics schemes can give important insights into the
propagation of aerosol effects in the cloud microphysics
(Glassmeier and Lohmann, 2016). This kind of analytical approach works
well for warm-phase clouds but is less conclusive for the response of
mixed-phase clouds, especially deep convective clouds, due to many
compensating effects and the complexity of the processes involving ice-phase
hydrometeors (Glassmeier and Lohmann, 2016).

Convective invigoration
(Andreae et al., 2004; Rosenfeld et al., 2008; Lebo and Seinfeld, 2011) has been
proposed as a mechanism by which aerosols impact the development of deep
convective clouds. A higher number concentration of aerosols suitable for
acting as cloud condensation nuclei (CCN) can lead to more but smaller cloud
droplets, which are less likely to be processed into rain and precipitated
out of the cloud. This would lead to more water reaching the freezing level
in the cloud where subsequent freezing leads to additional latent heating in
the higher levels of the cloud, enhancing the strength of the convection with
higher updraft speeds and cloud-top height. Other studies point out the
additional impact of the larger number of aerosols, and subsequently cloud
droplets, leading to smaller ice particles, which then favours increased
cloud fraction, cloud-top height, and cloud thickness
(Fan et al., 2013) due to reduced fall speeds of the ice particles.
This implies a significant radiative effect on the climate system through
enhanced anvils (Koren et al., 2010).
Grabowski and Morrison (2016) argue that the effects can be purely
attributed to the effects of smaller droplets and ice crystals, with
negligible effects of the thermodynamic enhancement proposed in
Rosenfeld et al. (2008). Some of the differences in the assessments of
convective invigoration due to aerosols are actually caused by the difference
in the definition of both changes in aerosol and the quantification of the
strength of convection based on different variables such as surface
precipitation, updraft speeds or cloud-top heights
(Lebo et al., 2012; Altaratz et al., 2014). Significant mechanisms buffering the
impact of aerosols on clouds and precipitation, both with a focus on
warm-phase processes (Stevens and Feingold, 2009) and for mixed-phase and
ice clouds (Fan et al., 2016), have been proposed. However, recent studies
question the attribution of observed relationships between aerosol
concentrations and cloud-top height to aerosol microphysical effects
(Varble, 2018; Nishant and Sherwood, 2017). It is, therefore, one
of the main goals of this paper to investigate whether and how these proposed
mechanisms of convective invigoration, especially the proposed invigoration
of convection due to additional latent heat release from freezing, manifest
themselves in numerical simulations.

Many studies have pointed out the representation of cloud microphysics in
models as one of the main sources of uncertainty in high-resolution model
studies of aerosol–cloud interactions or cloud feedbacks to a warming
climate, especially for mixed-phase and ice-phase clouds
(Tao et al., 2012; Khain et al., 2015; White et al., 2017). This also
holds for the role of the microphysics schemes in global model simulations of
both convection and aerosol–cloud interactions
(Lohmann and Feichter, 2005; Gettelman, 2015; Malavelle et al., 2017).

Most currently used cloud microphysics schemes can be separated into two
approaches, bulk microphysics schemes and bin microphysics schemes
(Khain et al., 2015). Bulk microphysics schemes assume a specific
size distribution for a range of different hydrometeor classes and describe
their evolution and interactions based on a certain number of moments of
these distributions. Double-moment schemes with both prognostic mass and
number concentrations of the hydrometeors are the current standard and
necessary to meaningfully represent aerosol–cloud interactions
(Khain et al., 2015; Igel et al., 2014).

The separation of the hydrometeors into individual hydrometeor classes in
microphysics schemes brings with it specific challenges in resolving the
microphysical processes. In bulk schemes, liquid water in the cloud is
separated into cloud droplets and raindrops. The collision–coalescence
processes leading to the formation of rain from cloud droplets have to be
parameterised through the artificial process of droplet autoconversion and a
simplified treatment of accretion of droplets by raindrops. The
semi-empirical nature of these parameterisations has been shown to be the
source of major uncertainty in the assessment of aerosol–cloud interactions
in numerical model simulations
(Khain et al., 2015; White et al., 2017). In the ice phase, most
current microphysics schemes separate the hydrometeors into a number of
different classes such as pristine ice, snow, hail or graupel. The equations
and parameters for the calculation of the microphysical process rates as well
as important physical properties of the hydrometeors, such as shape, density
or the specific form of the size distribution, are specified for each
individual hydrometeor class. These choices additionally impact important
physical processes such as the fall speeds of hydrometeors in the calculation
of sedimentation or the radiative properties of the hydrometeors. This can
lead to abrupt changes to the evolution of the cloud due to a change in the
partition between the hydrometeor classes in the ice phase of the cloud
(Morrison and Milbrandt, 2014). There have been developments towards
overcoming the separation of ice hydrometeors into fixed individual classes
(Harrington et al., 2013a, b; Morrison and Milbrandt, 2014; Morrison et al., 2015)
by treating ice-phase hydrometeors as one single class with smoothly varying
physical properties, which have been implemented in both cloud-resolving
models and in global climate models. Nevertheless, most current applications
rely on microphysics schemes performing the separation into different
hydrometeor classes. Better understanding the possible effects and causes of
shifts in the hydrometeor partitions through the comprehensive analysis of
the microphysical pathways in the two bulk microphysics schemes is thus a
main focus of this paper.

Bin microphysics schemes represent the different hydrometeors in the cloud
through a number of individual size bins per hydrometeor class, thus allowing
for more flexible representation of the actual size distribution and the
interaction between the different size bins (Khain et al., 2015).
Due to the large number of simulated variables, however, this approach
results in high computational cost. One of the main benefits is avoiding the
artificial separation between cloud droplets and raindrops that causes
challenges in bulk microphysics schemes, for example in the form of a
parameterisation of the autoconversion processes
(Khain et al., 2015). The representation of ice-phase hydrometeors
in typical bin microphysics schemes, however, is based on separate
hydrometeor classes as in the bulk schemes, each individually resolving their
size distribution through a number of bins (Khain et al., 2015).
While many studies have proposed that bin-resolving microphysics schemes are
necessary to reliably represent possible microphysical aerosol effects on
convective clouds (Khain et al., 2004; Fan et al., 2012, 2016)
in model simulations, a large range of studies and applications, e.g. routine
numerical weather prediction (NWP), coupled simulations with a complex
aerosol and chemistry and global climate model simulations as well as a large
number of CRM-based studies of aerosol–cloud interactions apply bulk
microphysics schemes.

This study aims to unravel the underlying microphysical mechanisms
responsible for the large diversity of simulated aerosol effects on
convection through a comprehensive analysis of the propagation of aerosol
perturbations through microphysical pathways in different microphysics
schemes.

Tracking individual convective cells in the simulation makes it possible to
draw direct conclusions about the behaviour of individual convective cells in
the simulations, e.g. regarding their time evolution or the response to
changes in simulation parameters that go beyond the bulk average over the
simulation domain or the sum of all cloudy areas in the simulation. The
analysis of tracked cumulus clouds has been applied in previous studies
(e.g. Dawe and Austin, 2012; Heus and Seifert, 2013; Heiblum et al., 2016a, b)
with a focus on various aspects of convective clouds, including the effects
of aerosol perturbations on deep convection (Terwey and Rozoff, 2014).

We have implemented detailed microphysical process-rate diagnostics for
pathway analysis in the two double-moment microphysics schemes of
Morrison et al. (2009) and Thompson et al. (2004). We analyse the
cloud morphology and the spatial structure of the microphysical processes in
individual tracked convective cells. We display the microphysical process
rates in the form of scaled pie charts. This has been inspired by previous
studies using this type of visualisation of the spatiotemporal development of
physical processes for other applications. Schutgens and Stier (2014)
performed a pathway analysis for the aerosol processes in a global climate
model (ECHAM-HAM). Chang et al. (2015) applied a microphysical
pathway analysis including a similar visualisation of process rates to
simulations of pyro-convective clouds, however, using a much simpler
two-dimensional model for highly idealised individual clouds.

In addition to the detailed process-rate diagnostics, we derive important
bulk cloud properties, such as the total cloud mass or the altitude of the
centre of gravity, and analyse their evolution over the life cycle of the
tracked cells. Our approach goes beyond previous studies with a similar
set-up (Morrison et al., 2009; Kalina et al., 2014) that mainly focussed on
domain average properties and only a specific subset of microphysical
processes.

We represent idealised aerosol perturbations through changes to a fixed cloud
droplet number concentration (CDNC) in each simulation with the two bulk
microphysics schemes. This allows us to isolate the actual cloud
microphysical pathways from uncertainties in the representation of the
activation of CCN in numerical models
(Ghan et al., 2011; Simpson et al., 2014; Rothenberg et al., 2018).
Simulations are performed for a comprehensive range of CDNC for each
microphysics scheme ranging from values representative of very clean,
maritime conditions (CDNC =50cm−3) to very polluted situations
(CDNC =2500cm−3).

We compare the results to simulations performed with a bin microphysics
scheme (HUJI spectral-bin scheme) for a subset of the analyses to investigate
whether the effects investigated in more detail through the microphysical
pathway analysis for the two bulk microphysics schemes agree with the
response of a bin microphysics scheme to perturbations of aerosol proxies.

2.1 Model set-up

The simulations are performed with the Weather and Research Forecasting model
(WRF) version 3.7.1 (Skamarock et al., 2008). We use the two-moment
microphysics schemes from Thompson et al. (2004, 2008),
denoted as THOM, and from Morrison et al. (2005, 2009), called
MORR in our figures and tables. To isolate the role of cloud microphysics for
aerosol effects on deep convection from additional uncertainties in
model-simulated aerosol fields, we apply a fixed CDNC in the two bulk microphysics schemes for each simulation. In
each of the schemes, the CDNC is reset to the chosen value at the end of each
model time step in all cloudy grid points. We vary this CDNC value between
different simulations as a proxy for aerosol number concentration. There are
versions of both bulk microphysics schemes that include the activation of a
fixed CCN spectrum or even interactive aerosols
(Thompson and Eidhammer, 2014; Wang et al., 2013). However, the implementation of
both the cloud droplet activation and the representation of the aerosol
distributions is very different between the two microphysics schemes, which
would add additional differences between the schemes compared to representing
the perturbations in the form of a varying CDNC.

The detailed analyses of the process rates in this paper are carried out for
simulations using the two bulk microphysics schemes. To investigate how the
results obtained from the detailed analysis of the two bulk microphysics
schemes hold for a bin cloud microphysics scheme, we also include additional
simulations with the Hebrew University cloud model (HUCM) spectral-bin
microphysics scheme
(Khain et al., 2004; Lynn et al., 2005a, b), called SBM in
the rest of the paper. We perform a subset of the analyses for this
microphysical scheme, excluding the detailed microphysical process-rate
analysis but including the analysis of changes to the hydrometeor mixing
ratios and the bulk cloud properties. We use the full version of the
spectral-bin microphysics scheme in WRF (Khain et al., 2012) and perform a
variation of CCN number concentration.

Both bulk microphysics schemes make use of saturation adjustment, removing
all water vapour exceeding the saturation vapour pressure in each time step
and instantaneously condensing it to cloud water at each time step. This
prevents a build-up of supersaturation in strong updrafts and can thus impact
effects of perturbations in the microphysics (Lebo et al., 2012). The bin
microphysics scheme (SBM) includes an explicit calculation of supersaturation
in the microphysics at each time step and allows for a build-up of
supersaturation in strong updrafts over several time steps.

We simulate two different idealised supercell cases. The first set of
simulations (CASE1) is based on the default WRF quarter-circle shear
supercell case representative of a supercell case over the southern Great
Plains of the United States (Khain and Lynn, 2009; Lebo and Seinfeld, 2011).
This case uses an initial sounding described in Weisman and Klemp (1982)
with a surface temperature of 300 K and a surface vapour mixing ratio
of 14 g kg−1. The wind profile is taken from
Weisman and Rotunno (2000) and features a wind shear of 40 m s−1 made
up of a quarter-circle shear up to a height of 2 km and a linear
shear further up to 7 km height. The initiation of convection is
triggered by a warm bubble with a magnitude of 3 K in potential
temperature centred at 1.5 km height in the centre of the domain with
a radius of 10 km horizontally and 1.5 km vertically in which
the perturbation decays with the square of the cosine towards the edge of the
bubble (Morrison, 2012). This type of set-up has been used for
a number of similar studies in the past
(Storer et al., 2010; Morrison and Milbrandt, 2010; Morrison, 2012; Kalina et al., 2014).

To test the representativeness of the results for different cases of
idealised deep convection, a set of simulations for a second supercell case
(CASE2) is based on an observed supercell storm over Oklahoma in 2008
(Kumjian et al., 2010). In contrast to the first case, the initial
profiles are from observations used in the model experiments in
Dawson et al. (2013). This case features a significantly drier initial
profile with a surface temperature of 308 K and a surface water
vapour mixing ratio of 16 g kg−1 along with wind shear of similar
magnitude to CASE1. The initiation of convection in this case is created by
forced convergence near the surface based on nudging the vertical velocity
over the same volume that is used for the warm bubble in CASE1. The
methodology is described in detail in Naylor and Gilmore (2012) and we use
an updraft speed peaking at 5 m s−1 at the centre of the volume.

Both cases are simulated without a boundary layer scheme and the calculation
of surface fluxes or radiation. The horizontal grid spacing of the
simulations is 1 km to sufficiently resolve the main features of the
simulated supercell. We use a model domain size of 84 grid cells in each
horizontal dimension and open boundary conditions on each side of the
modelling domain. The vertical resolution of the 96 model layers varies from
about 50 m at the surface to 300 m at the top of the model.
Simulations are performed with a time step of 5 s. The standard model
diagnostics and the microphysical pathway diagnostics
(Sect. 2.3) are output every 5 min to sufficiently
resolve the development of the microphysical processes during the life cycle
of the deep convective clouds.

Figure 1(a) Illustration of the result of the tracking and
watershedding methodology after 90 min of simulation time with the total
water path field in blues and contours of column maximum vertical velocities
in greens. The filled circles represent the tracked updraft cores, while the
empty circles show the position of the centre of gravity determined by the
watershedding algorithm. Crosses denote the slices along/across the line of
travel of the cell that are used for the analysis of the cloud morphology.
The coloured contour lines represent the projection of the respective cloud
mask for each cell to the surface. (b) Three-dimensional rendering
of the 1 g kg−1 condensate mixing ratio threshold of the two
tracked cells in the simulation at the same point in time, including the
horizontal location of the tracked updraft (cross) and centre of gravity
(dot).

2.2 Variation of aerosol proxies: CDNC or CCN

We analyse the effects of varying the CDNC in the two bulk microphysics
schemes to isolate the impact of microphysical pathways. We use a CDNC of
250 cm−3 as a baseline simulation. Simulations are performed for
two CDNC values corresponding to a cleaner environment than the baseline
simulation (50 and 100 cm−3) and five values representing more
polluted conditions (500, 1000, 1500, 2000 and 2500 cm−3).

For the simulations with the spectral-bin microphysics scheme, activation of
aerosols to cloud droplets is calculated from a CCN spectrum following the
equation NC=N0⋅Sk, with the prognostic supersaturation
S, the particle number concentration N0 and an exponent k. The
exponent is kept fixed at k=0.5, while N0 is varied in a range from 75
to 6750 cm−3. This yields cloud droplet number concentrations with
median values spanning a similar range to those chosen for the two bulk
microphysics schemes (Table 1).

Table 1Overview of the 52 simulations performed in this study, including
the two cases simulated and the different CDNC/CCN values for each of the
microphysics schemes. The CDNCs for the SBM simulations are the median values
for grid points with a cloud water mixing ratio larger than
10 g kg−1. Bold values of CDNC and CCN show
parameters that were set in the simulation setup; the CDNC values for the SBM
were diagnosed from the simulation results.

2.3 Pathway analysis

We have extended two double-moment bulk microphysics schemes, the Morrison
scheme (Morrison et al., 2005, 2009) and the Thomson scheme
(Thompson et al., 2004, 2008) in WRF 3.7.1, by writing
detailed microphysical pathway diagnostics at each output time step. This
includes all individual process rates for both hydrometeor mass and
hydrometeor number mixing ratio as well as individual latent heating rates
for the three phase transitions (liquid–vapour, liquid–ice, ice–vapour)
and the hydrometeor mass and number tendencies for the individual hydrometeor
classes (cloud water, rain, cloud ice, graupel, snow) are diagnosed at every
output time step.

For most analyses in this study, the individual microphysical processes are
grouped into a consistent set of classes according to their contribution to
the hydrometeor mass transfer in the model. This includes the six different
phase transitions between frozen hydrometeors, water drops and water vapour
(condensation, evaporation, freezing including
riming, melting, deposition and sublimation) as
well as the warm rain formation due to autoconversion and accretion
of cloud droplets and all processes that transfer mass between the different
frozen hydrometeors as ice processes. For some of the more detailed
analyses, this grouping is performed in a more detailed way, e.g. separating
freezing and riming processes or splitting them up by the specific
hydrometeor class involved in the transfer. A collection of all the
individual microphysical process rates represented in the two bulk
microphysics schemes including the grouping discussed here is given in the
Appendix (Table B1 for the Morrison microphysics
scheme and in Table B2 for the Thompson
microphysics scheme).

2.4 Convective cell tracking

We have developed a tracking algorithm focussed on the tracking of individual
deep convective cells in CRM simulations, but flexible enough to be extended
to other applications, e.g. simulations of shallow convection or based on
geostationary satellite observations using brightness temperature data. The
initial tracking of features is performed on the column maximum vertical
velocity at each output time step using Python tracking library trackpy
(Allan et al., 2016). These features are then filtered and linked to
consistent trajectories. The trajectories are extrapolated to two additional
output time steps at the start and at the end to allow for the inclusion of
both the initiation of the cell and the decaying later stages of the cell
development.

Based on these trajectories, a three-dimensional watershedding algorithm,
morphology.watershed from the Python image processing
package scikit-image
(van der Walt et al., 2014), is applied to the total condensed water content
field (mass mixing ratio of all hydrometeors) at each output time step to
infer the volume of the cloud associated with the tracked updraft. We use a
threshold of 1 g kg−3 to define the core cloudy grid points in
the simulations. A variation of this threshold by up to an order of magnitude
to 0.1 g m−3 only showed minor changes to the results of the
study.

A separate watershedding is performed for both liquid water content (cloud
droplets and rain drops) and ice water content (all ice hydrometeors). This
allows for the determination of the centre of gravity and the mass, for the
entire cloud as well as for the in-cloud liquid and frozen phases,
respectively. The evolution of the centre of gravity has been studied mainly
for warm convective clouds
(e.g. Koren et al., 2009; Dagan et al., 2015, 2017, 2018)
and with a focus on the warm phase of deep convective clouds
(Chen et al., 2017).

The tracking algorithm does not explicitly treat splitting and merging of
convective cells. In all simulated cases in this study, the initial
convective cell splits into two separate counter-rotating cells early into
the simulations. In CASE1 this leads to a relatively symmetric situation with
similarly strong individual cells. In both cases, one of the cells develops
more directly out of the initial cell: in CASE1 this is the right-moving
cell, while in CASE2 this is the stronger left-moving cell. In each
simulation, this stronger cell gets picked up as a continuation of the
initial cell by the tracking algorithm. The second cell has been analysed
following the same methodology and showed very similar results in all major
aspects. We have thus decided to focus on the analysis of the first cell in
this paper and to not discuss the results from the second cell in more
detail.

Microphysical process rates, latent heating rates and other cloud
microphysical parameters such as hydrometeor mixing ratios are summed up for
regularly spaced altitude intervals in the volume of the individual cells to
get representative profiles for each cloud. We interpolate the microphysical
process rates and other variables used in the analysis to slices along and
perpendicular to the line of travel of the cell
(Fig. 1) to visualise and analyse the morphology of
the cells for different simulation set-ups and at different stages of the
cloud life cycle.

3.1 Baseline simulations

Figure 2Cloud microphysical morphology along a slice parallel
to the cell track for a cloud droplet number concentration of
250 cm−3 for the Morrison microphysics scheme. The
area of each specific colour in the pie charts is proportional
to the water turnover (a)–(c) in kgm-3s-3 and
latent heating (d)–(f) in W m−3 for the process rates
and to the mass mixing ratio for the hydrometeors (g)–(i). Contour
lines denote the mixing ratio threshold of 1 g kg−1 for liquid (blue)
and frozen (grey) water content as well as the melting level (0 ∘C
isotherm). Arrows denote the wind field with updrafts in red
and downdrafts in blue.

The simulations with CDNC =250cm−3 for both bulk microphysics
schemes (Figs. 2
and 3) are used as a baseline simulation
representative of intermediate aerosol loading. As for all the following
figures for CASE1, these analyses are based on a combination of the initial
stage of the cell and the right-moving cell after the cell split. We use
three different points in time (15, 25 and 60 min) to illustrate the
microphysical evolution of the cell in simulations with the two different
microphysics schemes.

During the initial phase of the formation of the convective cloud in the
simulation using the Morrison bulk microphysics scheme
(Fig. 2a, d, g), the two major
microphysical processes are condensation to form cloud droplets and rain
formation from these droplets, while the top of the cloud at around
7.5 km is already influenced by freezing and riming processes. The
simulation with the Thompson microphysics scheme shows a similar development
during the initial cloud stage
(Fig. 3a, d, g). The initiation of
freezing at the top of the cloud is slightly delayed in comparison to the
simulation with the Morrison scheme. During the next 10 min, the cell
quickly intensifies, dominated by the development of rain formation
(autoconversion of cloud droplets and accretion of cloud droplets by rain)
between 4 and 7 km. Freezing occurs at a height of about
7–8 km. After an hour of simulation, the cell has developed into a
mature supercell with hail dominating the mass mixing ratio in the ice phase.
A significant amount of cloud droplets extends up to 10 km height.
Rain formation and freezing occur in the region of the strongest updraft with
a width of about 5 km for both microphysics schemes. During the later
stage, the freezing in the simulation using the Morrison microphysics scheme
takes place over a substantial vertical range and is strongest at both edges
of the mixed-phase region of the cloud at around 8 and 10 km altitude
(Fig. 2c). The Thompson scheme instead
shows a more confined region of freezing. In both bulk microphysics schemes,
condensation processes dominate the latent heat release in the cloud for all
stages of the cloud development
(Figs. 2d–f, 3d–f).
In the mature stage of the cell, the main difference in the hydrometeor
classes between the two microphysics schemes is an enhanced presence of snow
both in the core and in the anvil for the Thompson microphysics scheme
(Figs. 2i
and 3i).

3.2 Effects on cloud morphology and microphysical process rates

Figure 4Cloud microphysical morphology along a slice through the
cloud parallel to the track of the cell for simulations with three
different CDNC values (a, d: 50 cm−3, b, e: 2500 cm−3,
c, f: 2500 cm−3) after 60 min of simulation using the
two bulk microphysics schemes (a–c: Morrison, d–f: Thompson).

We first investigate changes to the right-moving cell in CASE1 due to a
variation of CDNC. We focus on three different CDNC values (clean, baseline,
polluted; see Fig. 4) after 60 min of
simulations using the two bulk microphysics schemes. In the microphysical
process rates, a decrease in rain formation from droplets (autoconversion and
accretion) with increasing CDNC is evident in the core of the cell for both
bulk microphysics schemes. For both bulk schemes, the freezing and riming
processes are shifted upwards with increasing CDNC. The mixed-phase region of
the cloud, indicated by the liquid water mixing ratio contour in
Fig. 4, extends about 1–2 km higher
in the polluted case for each bulk scheme.

In the hydrometeor mass mixing ratios
(Fig. 5), an increase in cloud droplet
mass at the expense of raindrops for increasing CDNC is evident in both bulk
microphysics schemes and the spectral-bin microphysics scheme, particularly
in the mixed-phase region of the cloud at around 6–8 km. In the
Thompson scheme, most of the ice-phase hydrometeor mass is present in the
form of snow for the high CDNC simulation
(Fig. 5d), especially towards the cloud
top and in the anvil region, while graupel dominates except in the anvil for
the cleanest case (Fig. 5c). In
contrast, the ice phase in the Morrison scheme shows a high hail mixing ratio
for low and high CDNC values
(Fig. 5a, b) and additional ice
particles, but only small amounts of snow in the simulation with the highest
CDNC value. The simulations using the spectral-bin microphysics scheme
(Fig. 5e, f) show a stronger increase
in cloud droplet mass mixing ratio than the two bulk schemes for increased
CCN. Graupel and hail, the predominant ice-phase hydrometeors in the cleanest
simulation, get replaced by cloud-ice particles for the highest CCN value.
However, it has to be taken into account that the definition of the
hydrometeor classes differs between the three different microphysics schemes.

Figure 6 provides a vertically resolved view of the
time evolution of the microphysical process rates over the life cycle of the
right-moving cell for the two bulk microphysics schemes under the cleanest
and most polluted conditions. For both schemes, a strong decrease in the warm
rain formation processes (autoconversion of cloud droplets and accretion of
cloud droplets by rain) with increased CDNC can be observed. This even leads
to a complete shut-down of warm rain production in the Thompson scheme, which
is also evident in the absence of rain hydrometeors in
Fig. 4. As a result, evaporation in the
lowest model levels decreases strongly for the high CDNC value in the
simulations with the Thompson scheme. Both microphysics schemes show a
significant decrease in the total amount of melting of frozen hydrometeors
below the melting line at about 4 km height. The strong cooling due
to evaporation and melting in the cleanest cases for the simulations with the
Thompson scheme (Fig. 6c) can explain the
significantly shorter lifetime of the cell compared to the more polluted
cases and the other bulk scheme. The dominant region of freezing processes is
lifted from around 8 km height in the low CDNC case to around
10 km for the high CDNC case height in both schemes. While deposition
on ice hydrometeors is a significant process for all values of CDNC for the
Morrison scheme, it becomes more enhanced for the most polluted simulation
using the Thompson scheme, related to the change in the dominant ice-phase
hydrometeor class to snow (Fig. 5).
Condensation onto cloud droplets is present in all simulations up to
10 km height in comparable amounts and dominates the latent heating
due to the large energy transfer involved. Deposition processes onto ice
hydrometeors are significant for both the cleanest and the most polluted
simulation in the Morrison scheme, while the Thompson scheme shows much more
deposition in the most polluted case, which can be related to the changes in
the hydrometeor composition (Fig. 5).
The decrease in the total amount of microphysical mass transfer in all
simulations around 55 min into the simulations is caused by the splitting of
the tracked cell into two individual cells. However, no significant change to
the relative proportions of the different processes can be observed at this
stage.

Figure 5Hydrometeor mass mixing ratios in a slice along the line of travel
of the cell for the cleanest (a, c, e) and most polluted (b, d, f) simulations
after 60 min of simulation for the three microphysics schemes in CASE1.

Figure 6Time evolution of the microphysical process rates for the
cleanest (a, c) and most polluted (b, d) simulations and the two
bulk microphysics schemes (Morrison:
a, b, Thompson: c, d) in CASE1. The pie charts denote mass transfer summed up over the
volume of the cloud in each altitude interval for the different groups of microphysical
process rates with the area of each colour
proportional to the mass transfer. The red line shows the
height of the 0 ∘C isotherm.

A more detailed analysis of the processes involved in the formation of rain
over the lifetime of the cell in the different cases
(Fig. 7) reveals that autoconversion of cloud
droplets to rain for the highest CDNC values in both bulk schemes is almost
negligible, with only very little autoconversion in the Morrison scheme, even
for the smallest CDNC value. Accretion of cloud droplets by rain is strongly
depressed for high CDNC in both microphysics schemes. Melting of ice
hydrometeors contributes significantly to the production of rain in both bulk
schemes and is reduced for the high CDNC case, especially in the Thompson
scheme.

The processes transforming liquid to frozen water can be further broken down
into processes representing the freezing of individual cloud droplets or
raindrops and riming processes, in which existing ice-phase hydrometeors
accrete liquid water (Fig. 8). For both bulk
microphysics schemes, freezing of raindrops and cloud droplets occurs in two
separate layers, with freezing of raindrops at around 8 km and
freezing of cloud droplets above a height of 10 km up to
14 km. In both microphysics schemes, freezing of raindrops is
strongly decreased for increased CDNC
(Fig. 8b, d), while freezing of cloud
droplets is increased by about a factor of 3. This is not related to the
parameterisation of the freezing processes (described in more detail in
Appendix B), which does not include any
information about cloud droplet effective radius and raindrop effective
radius through the number concentrations. Instead, these changes are purely a
result of the shift in the abundance of cloud droplets and raindrops
(Fig. 5).

The riming processes are spread out over a much larger altitude range in the
cloud, between the melting level at about 4 km and about
11 km height for riming of cloud droplets and below 9 km for
the riming of raindrops. Riming is significantly stronger at all CDNC values
in the simulations with the Morrison scheme
(Fig. 8a, b). In the Morrison scheme, riming
of rain droplets is strongly decreased for higher CDNC and mainly restricted
to around 5 km height. In the Thompson microphysics scheme
(Fig. 8c, d), raindrop riming is also
strongly decreased for high CDNC, but still occurs over the same height range
as in the low CDNC case. Both microphysics schemes show a slight increase in
droplet riming with higher CDNC over the entire altitude range. We can thus
explain the shift in freezing and riming processes observed in
Fig. 6 by a decreased riming of rain droplets at lower
altitudes and a shift from the freezing of raindrops to the freezing of cloud
droplets occurring at higher altitudes.

The evolution of the deposition and sublimation processes
(Fig. 9) shows substantial
differences between the two bulk microphysics schemes and a strong response
to a variation of CDNC. The calculation of deposition and sublimation in the
microphysics scheme is explicitly parameterised for each hydrometeor class,
taking into account detailed information on the size distribution of the
hydrometeors (Thompson et al., 2004; Morrison et al., 2005). In the Morrison
scheme (Fig. 9a, b), the
increase in CDNC leads to a decrease in both deposition and sublimation over
the entire height of the cloud. These processes dominantly occur on hail for
the cleanest case and are more distributed over hail, snow and pristine ice
in the polluted case, which agrees with the shifts in the hydrometeor mixing
ratios (Fig. 5a, b).

In the simulations with the Thompson microphysics scheme
(Fig. 9c, d), deposition and
sublimation processes show a very different behaviour. The strong increase in
snow in the cloud with increasing CDNC
(Fig. 5c, d) leads to a strong increase
in both deposition and sublimation on snow. Deposition on ice is of the same
order of magnitude for the cleanest case, but is not strongly affected by a
change in CDNC. Sublimation of graupel only occurs around and below the
melting layer and is significantly reduced by increasing CDNC. As deposition
on graupel is prohibited in this microphysics scheme, there is no decrease in
deposition on graupel associated with the changes in the hydrometeor ratio
compensating the increase in deposition on snow. This leads to a strong
increase in total deposition with increased CDNC as the main response in the
Thompson scheme.

Figure 7Time evolution of the microphysical process rates
relevant for rain formation processes (autoconversion, accretion
of cloud droplets by rain and melting of ice hydrometeors) as in
Fig. 6.

Latent heating constitutes a key feedback of the microphysics scheme onto the
model dynamics along with changes to the buoyancy due to changes in
condensate loading. The vertically resolved latent heating over the lifetime
of the tracked cell in CASE1 is shown in
Fig. 10 for all three microphysics schemes
and split up into the individual phase changes for the two bulk microphysics
schemes in Fig. 11.

Latent heat release from condensation is the dominant contribution to the
latent heating and about a magnitude stronger than the other contributions,
thus determining the general shape of the latent heating profile
(Figs. 10
and 11a, g). The changes to condensation due to
changes in CDNC in the two bulk microphysics schemes are comparatively small,
which can be explained by the use of saturation adjustment in the calculation
of the condensation, which does not include an effect of changes in droplet
radius on the condensation.

The same limitation applies to the evaporation of cloud droplets, which also
cannot show any direct effect from changes in CDNC due to the use of
saturation adjustment. However, the evaporation shows much stronger
differences between the two microphysics schemes and also a stronger effect
of a variation in CDNC (Fig. 11b, h). The strong
changes in the evaporation at higher levels in the mixed-phase region of the
cloud, especially for the Thompson scheme, can be explained with the changes
in deposition on frozen hydrometeors (Fig. 11e, k).
The increased deposition with increasing CDNC through the changes to the
frozen hydrometeors could lead to a further decrease in the saturation vapour
pressure over water in the water-subsaturated regions of the cloud and thus
additional evaporation. There is also a noticeable decrease in condensation
in the higher layers of the mixed-phase region of the cloud at around 10 km
for the Thompson scheme (Fig. 11g), which could be
similarly related to the increase in deposition. The evaporation in the lower
layers is associated with the evaporation of raindrops. The differences
between the two schemes and the variation with changes in CDNC can be
directly related to the differences in the amount of rain, which is both
higher and more strongly decreasing with increasing CDNC in the Thompson
scheme than in the Morrison scheme.

Figure 9Time evolution of the microphysical process rates of deposition
and sublimation as in Fig. 6.

All three microphysics schemes show a small shift of latent heating to higher
altitudes superimposed on that in the range between 7 km and about
10 km for increasing CDNC (Fig. 10),
which can be associated with the shifts in freezing and riming
(Fig. 11d, i), described in more detail in
Fig. 8. The decrease in latent cooling from
melting processes in the lowest layers is stronger in the Thompson scheme
than in the Morrison scheme (Fig. 11b, h).

There are large differences between the microphysics schemes in the latent
heating and cooling from sublimation and deposition and their response to
changes in CDNC. The Morrison scheme shows a significant decrease in both
sublimation and deposition with increased CDNC
(Fig. 11e, f). Apart from changes due to the shift
in hydrometeors from hail to snow and cloud ice
(Figs. 5
and 9), these decreases can be
related to the lower amount of ice hydrometeors in the mixed-phase region of
the cloud. Although these two changes cancel each other to a large extent in
the integrated latent heating, the two processes occur at different heights,
which results in a shift of latent heating to lower levels, opposing the
changes to the freezing and riming processes
(Fig. 11c). Furthermore, this strong decrease in
sublimation leads to a decrease in water vapour near the cloud base, which
could cause the consistent decrease in condensation at around 5 km
altitude in the Morrison scheme (Fig. 11a).

In the Thompson scheme, sublimation of ice hydrometeors is weak and barely
affected by changes in CDNC (Fig. 11l). However,
increases in CDNC lead to an increase in deposition in the higher parts of
the cloud (Fig. 11k). This effect can be explained
by the observed shift in hydrometeors from graupel to cloud ice and snow
since deposition on graupel is turned off in the Thompson microphysics
scheme, while it occurs on both snow and cloud ice. This increase in
deposition could be the main reason for the changes observed in evaporation
of cloud droplets as it significantly increases the sub-saturation over water
in the mixed phase in regions that are supersaturated with respect to ice.
This can be interpreted as a manifestation of the
Wegener–Bergeron–Findeisen process
(Wegener, 1911; Findeisen, 1938; Findeisen et al., 2015; Storelvmo and Tan, 2015),
transferring water mass from liquid hydrometeors to the frozen hydrometeors.
This constitutes an additional feedback from the changes in the ice phase
back onto the liquid-phase hydrometeors.

In contrast to the increased latent heating from freezing or melting, changes
in condensation and evaporation, as well as in sublimation and deposition,
are linked to a change in condensate loading, which affects the buoyancy of
the cloud and thus at least partially buffers the impact of latent heating
and cooling on the dynamics of the clouds.

The changes to the vertically integrated latent heating in the cloud for all
three microphysics schemes do not show a significant trend with increasing
CDNC (Fig. 10d, e, f). The Thompson scheme
shows slightly higher integrated latent heating for the two simulations with
the highest CDNC content but no consistent trend over the rest of the
simulations (Fig. 10e). The SBM simulations
show a slightly decreasing trend of integrated latent heating for the highest
CDNC values above 1000 cm−3 but no consistent trend over the
entire range of values (Fig. 10f). Despite
the significant change to the altitude of freezing, there is no systematic
change in the integrated latent heat release from freezing for both bulk
microphysics schemes that would contribute to an invigoration of the cloud.
In the Morrison scheme, the strong changes in deposition and sublimation
almost entirely cancel out when integrated vertically. In the Thompson
microphysics scheme, the increase in the integrated latent heat release from
deposition cancels out the significant decrease in the integrated evaporation
of cloud droplets and rain.

Figure 10Profiles of the sum of latent heating over the lifetime
of the dominant tracked cell for the three microphysics schemes in CASE1.

3.3 Effects on cloud mass and centre of gravity

Figure 12Total water mass, liquid water mass and frozen
water mass in the analysed right-moving cell for the three different
microphysics schemes (Morrison: a, d, g, Thompson:
b, e, h, SBM: c, f, i) in CASE1.
The jump in the curves occurs at the point where the cell splits into two individual cells.

The tracking and watershedding allow for a determination of the cloud mass
inside the identified cloud volumes and the centre of gravity of the
hydrometeors in the cloud. These analyses are also performed separately for
the liquid-phase and ice-phase hydrometeors in the cloud, which allows us to
relate the changes in the properties for the entire cloud to changes in the
individual phases.

The evolution of the cloud mass and the mass of the two water phases in the
cloud (Fig. 12) in the three microphysics schemes is
similar, with a maximum cloud mass of about 2×1010kg for
all microphysics schemes before the splitting of the cell and then about 1.5×1010kg for the two bulk microphysics schemes
(Fig. 12a, b) and slightly higher cloud masses of up to
1.8×1010kg in the spectral-bin microphysics scheme
(Fig. 12c). The cloud mass and also the difference between
the bulk schemes and the bin scheme are dominated by the ice-phase
hydrometeors, while the liquid-phase mass is very similar in all three
different microphysics schemes, making up about 20 %–25 % of the total
cloud mass.

Figure 13Altitude of the centre of gravity of the cloud and the individual phases
in the analysed right-moving cell for the three different microphysics schemes (Morrison: a, d, g,
Thompson: b, e, h, SBM: c, f, i) in CASE1.

There are, however, marked differences in the response to changes of the
aerosol proxy between the microphysics schemes. The Morrison scheme shows a
decrease in total cloud mass and ice-phase mass by about 10 %–15% over
the range in which we increase the CDNC and no significant changes in the
liquid phase. This decrease in ice-phase mass can be directly linked to the
changes in the microphysical process rates analysed in
Sect. 3.2. The shift of freezing to higher
altitudes leads to a reduction in frozen hydrometeors in the mixed phase of
the cloud and thus significantly less growth of the ice phase through vapour
deposition. In the Thompson scheme, however, increased CDNC leads to an
increase in ice-phase and total mass and a small increase in cloud liquid
mass. This increase agrees well with the increased deposition due to the
changes in the ice hydrometeor partition in the cloud discussed in
Sect. 3.2. In the simulations using the SBM
scheme, the two phases show a differing response to the aerosol proxy with
increased liquid hydrometeor mass and a decrease in ice-phase mass for
increasing CCN.

The altitude of the centre of gravity is affected by the choice of
microphysics scheme, with an overall higher centre of gravity for the SBM
scheme (Fig. 13c) compared to the two bulk microphysics
schemes (Fig. 13a, b).

There is a consistent response in the cloud heights for all three
microphysics schemes. The microphysics schemes show an increase in the height
of the centre of gravity of the entire cloud, which is more pronounced using
the Thompson scheme (about 1.5 km) than in the Morrison scheme (about
0.5–1 km). This includes an upward shift in both the liquid and
frozen water in the cloud. The increased height of the liquid phase can be
directly related to the decrease in the formation of warm rain
(Fig. 6) and the more numerous cloud droplets reaching
higher up in the cloud in the polluted case compared to the dominating
raindrops in the cleanest case
(Fig. 5). The increase in the altitude
of the ice phase in the cloud with increased CDNC can be related to the
changes in the altitude of the freezing processes. However, it can also be a
result of the lower fall speeds of the ice and snow hydrometeors dominating
in the polluted case instead of graupel and hail in the cleanest cases. As
for the bulk microphysics schemes, there is an increase in the height for
both phases in the simulations using the SBM scheme, which is significantly
more pronounced in the liquid phase of the cloud.

All three microphysics schemes show a clear saturation in the effect of
changes in the CDNC/CCN concentration. Variations above 2000 cm−3
in the bulk schemes and above 1350 cm−3 in the SBM simulations
only lead to insignificant effects on both the cloud mass and the altitude of
the centre of gravity of the different phases.

3.4 Sensitivity test: a second idealised supercell case (CASE2)

Figure 14Temporal evolution of the microphysical process rates
in CASE2 for the cleanest (a, c) and most polluted (b, d) simulations
and the two bulk microphysics schemes (Morrison: a, b, Thompson: c, d).
The pie charts denote the different groups of microphysical process rates
with the area proportional to the sum of the microphysical process rates
in the specific altitude interval inside the cloud volume.

Figure 16Altitude of the centre of gravity of the cloud and the individual
phases in the analysed left-moving cell for the three different
microphysics schemes (Morrison: a, d, g, Thompson:
b, e, h, SBM: c, f, i) in CASE2.

To investigate the representativeness of the results and the response of the
deep convective clouds to the variation of aerosol proxies CDNC and CCN, the
same set of simulations and analyses have been performed for a second
idealised supercell case (CASE2) with different forcing and initial
conditions (Sect. 2.1).

The time evolution of the cloud-averaged process rates for the two bulk
microphysics schemes (Fig. 14) shows that
the total microphysical water transfer is much weaker in CASE2 than in CASE1,
with process rates about a factor of 3 smaller. This case shows much stronger
differences between the two bulk microphysics schemes in the general
evolution of convection. For the Morrison microphysics scheme, a development
of the convective cloud in two stages occurs. After an initial maximum in the
microphysical processes after around 30 min of simulation time, the
convective activity becomes weaker before picking up again after about an
hour of simulation time. For the Thompson microphysics scheme, this second
episode of development in the tracked cell is completely absent for all
simulations, with the cloud dissipating after about 60 min of simulation
time. This is potentially related to the substantially higher cooling at and
below cloud base due to the evaporation of rain and the melting of frozen
hydrometeors. The cooling can substantially weaken the convective updraft and
thus prevent the further development of the cell that takes place in the
simulations using the two other microphysics schemes. This finding agrees
with a substantially shorter lifetime of the cleanest case for the
simulations with the Thompson scheme in CASE1
(Fig. 6).

Despite these differences in the evolution, CASE2 shows very similar changes
in the microphysical processes due to a variation of CDNC to CASE1 for both
microphysics schemes. The formation of rain due to autoconversion of cloud
droplets and accretion by rain is smaller and restricted to lower heights in
the polluted case using the Morrison microphysics scheme. For the Thompson
microphysics scheme, the formation of rain is decreased and shifted to higher
levels in the model under polluted conditions. Furthermore, the freezing and
riming processes predominantly occur at higher altitudes than in the clean
case for both bulk microphysics schemes.

In line with these changes to the microphysical process rates, the evolution
of the cloud mass in CASE2 (Fig. 15) is smaller
than in CASE1 for the two bulk microphysics schemes, with about half as much
hydrometeor mass in the cloud up to about 5×109kg. The
ice phase is more dominant, with the liquid phase of the cloud only
accounting for less than a quarter of the total cloud mass. The simulation
with the spectral-bin microphysics scheme shows a larger cloud mass than the
two bulk schemes for this case, only about 30 % smaller than in CASE1
(Fig. 15a, b, c), which includes much more frozen
hydrometeor mass than the two bulk microphysics schemes
(Fig. 15d, e, f), while liquid-phase mass is
similar between the three microphysics schemes
(Fig. 15g, h, i).

The effects of a variation of CDNC are quite similar to the ones seen in
CASE1 for the two bulk microphysics schemes
(Fig. 15a, b). The simulations with the Morrison
scheme show a relatively small decrease in cloud mass, while cloud mass
increased by about 15 % for the Thompson microphysics scheme. These changes
are almost entirely due to changes in the ice phase of the clouds with
insignificant effects of a variation in the liquid phase
(Fig. 15g, h) for both bulk schemes. The
simulations with the spectral-bin microphysics scheme, however, show an
opposite response compared to CASE1, with an increase in cloud mass of a
similar magnitude to the variation in the two bulk microphysics schemes
(Fig. 15c), which is dominated by changes in the
ice phase (Fig. 15f). There is a significant
increase of almost 50 % in cloud liquid mass in the earlier stages of the
cloud evolution (Fig. 15i) at around 25 min of
simulation time between the cleanest and the most polluted simulations with
the SBM scheme. This coincides with a delayed evolution of the ice phase
during that period of the developing cloud.

The changes in the altitude of the centre of gravity show less clear
relationships with changes in the aerosol proxies CDNC/CCN in this case for
the two bulk microphysics schemes. The Morrison scheme
(Fig. 16a, d, g) has the strongest variation in the
time evolution of the altitude of the centre of gravity, but generally shows
a decrease in the altitude for both the liquid and ice phases in the cloud.
In the Thompson scheme (Fig. 16b, e, h) increased
CDNC leads to an increase in the height of the centre of gravity of the
entire cloud and of both phases of water in the cloud. Similarly, increasing
CCN in the spectral-bin microphysics scheme
(Fig. 16c, f, i) leads to a strong increase in the
altitude of the cloud mass and the individual phases, with the COG of total
mass about 1.5 km higher in the most polluted case
(6750 cm−3) compared to the clean case (67.5 cm−3) and
an even stronger shift of up to 2 km in the liquid phase. All the SBM
simulations with a higher CCN value than about 1500 cm−3 lead to
relatively similar results, which means that the aerosol effects saturate at
this value.

We investigated the effects of changes in cloud droplet number concentration
(CDNC) and cloud condensation nuclei (CCN) concentrations on the development
of idealised simulations of deep convection to test proposed aerosol effects.
This includes different mechanisms of convective invigoration
(Rosenfeld et al., 2008; Lebo and Seinfeld, 2011; Fan et al., 2013; Grabowski and Morrison, 2016).
A combination of cell tracking and detailed process-rate diagnostics was used
to investigate the evolution and structure of the microphysical processes in
individual deep convective cells. We used three different cloud microphysics
schemes (two bulk schemes and one bin scheme) to investigate how the choice
of microphysics scheme affects these results. By covering a wide range of
values of CDNC/CCN representative of conditions from very clean to very
polluted, we were able to look for consistent responses of the clouds to
changes in these aerosol proxies and thus go beyond a simple comparison of
just clean and polluted conditions.

An increase in cloud droplet number concentration from values representing
clean conditions (CDNC =50cm−3) to strongly polluted
conditions (CDNC =2500cm−3) leads to a shift of freezing
processes to higher levels in both bulk microphysics schemes. Detailed
analyses of the individual process rates confirmed that this is indeed
related to a shift from freezing of rain to freezing of cloud droplets and a
decrease in riming of raindrops due to larger amounts of liquid water in the
form of cloud droplets instead of rain. This, in turn, can be related to the
changes in autoconversion and accretion in the warm-phase region of the
cloud. This is in line with the first step of the mechanisms proposed for
convective invigoration of deep convection due to an increase in aerosols
acting as CCN
(e.g. Rosenfeld et al., 2008; Lebo and Seinfeld, 2011; Fan et al., 2013; Altaratz et al., 2014).
These changes are concurrent and linked to changes in the prevailing
hydrometeors in the different parts of the clouds. Both bulk microphysics
schemes showed a strong increase in cloud droplet mass mixing ratio at the
expense of raindrops for increased CDNC. This shift leads to a significant
increase in the height of freezing and riming processes, which shifts the
latent heat release from freezing upwards by about 2 km. This response is
consistent between the different microphysics schemes and confirms earlier
studies that stated the importance of changes in the partition between rain
and cloud droplets in determining the evolution of freezing and riming
(Seifert and Beheng, 2006; Kalina et al., 2014). The simulations with the
SBM scheme show an upward shift in latent heating that is very similar to the
one observed for the two bulk schemes and associated with the lifting of the
freezing and riming processes. This confirms that the effect is not just an
artefact of the separate treatment of raindrops and cloud droplets in the
bulk microphysics schemes or the application of saturation adjustment. In the
ice phase of the clouds, there is a clear shift from mainly graupel or hail
in the low-CDNC simulations to larger fractions of snow and ice crystals in
the high-CDNC simulation.

A more detailed analysis of the different components of the latent heating
for the two bulk microphysics schemes shows a complex superposition of
changes to the different phase changes in the tracked cells. This confirms
results from previous studies on the effects of aerosols on supercells
(Khain et al., 2008; Morrison, 2012; Kalina et al., 2014) and other
deep convective clouds (Ekman et al., 2011) that pointed out a range of
compensating processes limiting convective invigoration and a strong
dependency on the environmental conditions in which the cloud develops.
Condensation and evaporation are the largest contributions to latent heating
and cooling in the cloud. The relative changes in these two processes due to
changes in the aerosol proxies are comparatively small, except for the
changes in the evaporation of rain due to the strong decrease in the
formation of rain. This is to be expected, as condensation and evaporation of
cloud droplets in the two bulk microphysics schemes are represented using
saturation adjustment, which does not include the effect of changes in cloud
drop radius on the condensation and evaporation processes. Saturation
adjustment has the potential to mask the effects of aerosols in highly
supersaturated strong convective updrafts as described, e.g. in
Lebo et al. (2012) and Fan et al. (2018). Lebo et al. (2012) argue
that saturation adjustment, as used in both bulk microphysics schemes in this
study, leads to an artificial increase in condensation in the lower levels of
the clouds, which would limit the effects of aerosol concentrations on
buoyancy in mid and high levels.

There are significant differences between the two bulk schemes in the
profiles of sublimation and deposition as well as in the response of these
processes to changes in CDNC. This can be attributed to different parameter
choices in the schemes. The strongest differences result from the fact that
deposition onto graupel hydrometeors is not allowed to occur in the Thompson
microphysics scheme, which leads to a strong increase in deposition due to
the replacement of graupel by the other ice-phase hydrometeors on which
deposition occurs. This strong increase in deposition additionally drives
changes in condensation and evaporation in the mixed-phase region of the
cloud via the Wegener–Bergeron–Findeisen process. By effectively removing
water vapour, this leads to a noticeable feedback on the evaporation and
condensation on cloud droplets that are intrinsically not affected by changes
in CDNC because of the use of saturation adjustment. It was also shown that
the melting of frozen hydrometeors contributes significantly to the formation
of raindrops, especially under high CDNC conditions, which forms an
additional important feedback of changes in the ice-phase onto the warm-phase
processes.

The changes to the individual components of integrated latent heating in the
cloud due to a variation of CDNC compensate each other in the two bulk
microphysics schemes. Hence, there is no significant change in the total
integrated latent heating in the cloud with changes in CDNC/CCN and no
thermodynamic invigoration from changes in the microphysics due to the change
in the aerosol proxies. This result is confirmed in the SBM simulations, that
also do not show any significant change in vertically integrated latent
heating for a variation of CCN. Therefore, the absence of convective
invigoration in the bulk microphysics schemes cannot be solely attributed to
the application of saturation adjustment.

The analysis of the clouds with respect to the total cloud mass and the
altitude of the centre of gravity showed some contrasting results between the
different microphysics schemes. There is a clear signal of a lifting of all
parts of the clouds to higher altitude under polluted conditions, probably
associated with the changes in the ice-phase hydrometeor partition. This
agrees with findings from, e.g. Fan et al. (2013), reporting
substantial changes to cloud height and even in the absence of convective
invigoration in the form of increased total latent heating in the cloud.
However, the analysis of cloud mass revealed opposing trends in the response
between the three microphysics schemes. There is no clear pattern in the
different responses to CDNC/CCN with regard to these bulk cloud properties,
with variations between the two bulk microphysics schemes often as large as
between the bulk schemes and the spectral-bin microphysics scheme, which
confirms the strong differences between microphysics schemes found in
previous studies
(Lebo et al., 2012; Khain et al., 2015; White et al., 2017).

The results for the first case (CASE1), based on
Weisman and Klemp (1982), are supported by the analysis of a second
idealised supercell case (CASE2), based on Kumjian et al. (2010) and
Dawson et al. (2013). The microphysical process-rate diagnostics
revealed similar changes in rain formation and the altitude of freezing and
riming processes for the two bulk microphysics schemes in this second case.
All three microphysics schemes showed that the effects of a variation of CDNC
or CCN saturate above a threshold value in both simulated cases. Variations
above a CDNC of around 2000 cm−3 in the bulk schemes and above a
CCN concentration of 1500 cm−3 in the bin microphysics scheme do
not lead to any further changes in the convective clouds with regard to cloud
condensate mass or altitude. This confirms results from previous studies such
as Kalina et al. (2014) that reported a saturation of aerosol effects at
similar values.

The pathway analysis developed for this study also includes the process rates
for the number concentrations of the different hydrometeors. This includes
processes like ice multiplication that could play an important role in better
understanding some of the possible pathways of aerosol effects on convective
clouds (Fan et al., 2013, 2016).

This work focused on the analysis of microphysical pathways of aerosol
effects on deep convective clouds in an idealised framework. To test the
robustness of the results under realistic scenarios, including potential
buffering mechanisms, we are currently applying our analysis framework to
large case study simulations of isolated convection over the area around
Houston, Texas, as part of the ACPC initiative (Aerosol, Cloud,
Precipitation, and Climate Working Group,
http://www.acpcinitiative.org, last access: 24 February 2019). We apply
the cell tracking algorithm and the analysis of the detailed process-rate
output developed in this study for a range of different cloud-resolving
models and contrasting aerosol conditions. In these simulations, the
individual deep convective clouds in the cloud field evolve and interact
freely, which allows for a thorough analysis of important aspects such as the
impact of aerosol conditions on the cell lifetimes or the statistics of the
cloud size spectrum. The introduction of parameters describing the entire
convective cell such as cloud mass and the position of the centre of gravity
can contribute to a meaningful analysis of cloud field simulations with a
large number of individual clouds.

The understanding of the detailed structure of microphysical processes in
individually tracked deep convective clouds and the analysis of the pathways
through which aerosol perturbations affect the deep convective clouds advance
our understanding of aerosol–cloud interactions. This can be used to inform
the parameterisation of microphysical processes and aerosol–convection
interactions in global climate models. Recent developments in the use of
global cloud-resolving models in climate research
(e.g. Ban et al., 2014; Seiki et al., 2014; Sato et al., 2018)
further motivate a detailed understanding of the pathways of aerosol effects
on convective clouds and the uncertainties in their representation in
numerical models.

The WRF model is publicly available at
http://www2.mmm.ucar.edu/wrf/users/ (WRF Community, 2000, last access:
24 February 2019). The code of the modified WRF model with the microphysical
pathway diagnostics for the two bulk microphysics schemes and the additional
second supercell case is available from the authors on request along with
postprocessing code for the process rate analysis in Python. The tracking
algorithm applied in this study has been developed into the tracking
framework tobac (Tracking and Object-Based Analysis of Clouds) hosted on
GitHub at https://github.com/climate-processes/tobac (last access:
24 February 2019). The version of the code used in this paper is available at
https://doi.org/10.5281/zenodo.2577047 (Heikenfeld, 2019). The tracking makes use of
the trackpy library (Allan et al., 2016).

The tracking algorithm tracks individual convective cells and their volume
based on the model output fields of vertical velocity and total condensate
mixing ratio. The tracking of maxima in the column vertical velocity field is
performed using trackpy (Allan et al., 2016). The algorithm from trackpy
that is used to identify the updraft features requires an initial assumption
for the size of the tracked object. We chose a diameter of 15 km to
represent the large convective updrafts in the supercell cases. Tracked
updrafts are required to exist for six output time steps, i.e. 30 min, to be
included in the analysis, which helps to exclude spurious features in
vertical velocity and thus focus on the analysis of properly developed deep
convective cells. We extrapolate by two time steps at the beginning and at
the end of each tracked trajectory to include a representation of the initial
development of the convective clouds and the evolution after the weakening of
the central updraft.

The volume of the convective clouds is determined by a watershedding
algorithm using a fixed threshold to determine the extent of the individual
clouds based on the tracked updrafts. We use a threshold of
1 g cm−3 for the total water content in this study, and a
variation of this threshold by an order of magnitude to
0.1 g cm−3 showed that choosing a lower threshold did not
significantly change the cloud volume and cloud mass or any of the more
detailed process analyses.

Tables B1 and B2 give
an overview of the microphysical process rates for the hydrometeor masses as
they are implemented in the two bulk microphysics schemes
(Thompson et al., 2008; Morrison et al., 2009) studied in this paper.

In the Thompson scheme, some of the process rates are defined as signed
variables representing two opposed processes. In these cases, we have used
the process-rate variable with the positive sign for the respective process
and ignored the values with the negative sign, which are covered by the
opposing process (e.g. PRG_RCG for riming of rain on graupel and
PRR_RCG for melting of graupel due to the collection by rain).
Condensation/evaporation processes and deposition/sublimation processes are
only defined through one combined process rate variable in the code. We have
thus added the process rates with a negative sign as a variable in our
diagnostics (e.g. E_PRW_VCD for the evaporation of droplets in addition
to PRW_VCD for condensation) to allow for independent analyses of these,
e.g. when aggregating the variables in space or time.

Ice multiplication according to the Hallet–Mossop process is implemented
differently in the two bulk microphysics schemes. In the Morrison scheme,
this is implemented as a direct transfer of water mass from the liquid phase
to ice particles and considered to be contributing to riming. In the Thompson
scheme, however, it forms a transfer from the frozen hydrometeor to new ice
particles and is thus part of the “ice processes”. Hence, these processes
are found in different categories in the two tables presenting the process
rates. As the actual mass transfer is negligibly small, this difference
between the schemes is not relevant for the analyses performed in this study.

The two bulk microphysics schemes differ in important parameters regarding
the different hydrometeor classes. The Morrison microphysics scheme is used
in its configuration that treats the dense frozen hydrometeors as hail with a
density of 900 kg m−3, while the simulations with the Thompson
microphysics used graupel with a density of 500 kg m−3. The
density of cloud ice, however, is higher in the simulations with the Thompson
scheme 890 kg m−3 compared to the Morrison scheme
(500 kg m−3), while snow density is set to 100 kg m−3
for both schemes. The Thompson scheme has a more complex treatment of the
snow hydrometeor class compared to the Morrison scheme, making use of a
combination of two size distributions and thus allowing for a variation of
the density over its evolution
(Field et al., 2005; Thompson et al., 2008). The fall speed
calculations are based on different equations in the two microphysics
schemes, all parameters for the hydrometeor classes are left at their default
values.

MH, BW, LL and PS designed the experiment, MH and BW implemented
the microphysical pathway analysis in WRF, MH set up the simulations and
developed the data analysis including the tracking algorithm, MH wrote the
manuscript and BW, PS and LL contributed to the analysis and the manuscript.

This article is part of the special issue “BACCHUS – Impact of
Biogenic versus Anthropogenic emissions on Clouds and Climate: towards a
Holistic UnderStanding (ACP/AMT/GMD inter-journal SI)”. It is not associated
with a conference.

Max Heikenfeld acknowledges funding from the NERC Oxford DTP in Environmental
Research (NE/L002612/1). The research leading to these results has received
funding from the European Union's Seventh Framework Programme (FP7/2007-2013)
project BACCHUS under grant agreement no. 603445 (Max Heikenfeld, Philip
Stier and Laurent Labbouz). The authors acknowledge funding from the European
Research Council project ACCLAIM (Philip Stier and Bethan White) under grant
agreement no. 28002 from the European Union's Seventh Framework Programme
(FP7/2007-2013). Philip Stier and Max Heikenfeld acknowledge funding from the
European Research Council project RECAP under the European Union's Horizon
2020 research and innovation programme with grant agreement 724602. Laurent
Labbouz has also been supported by CNES. Bethan White has also received
funding from the Australian Government through the Australian Research
Council. The authors would like to acknowledge the use of the University of
Oxford Advanced Research Computing (ARC) facility
(https://doi.org/10.5281/zenodo.22558) in carrying out this work. We want to thank Hugh
Morrison and Greg Thompson for important discussions about the two bulk
microphysics schemes used in the study and Matthew Christensen for helpful
comments on the manuscript.

Thompson, G. and Eidhammer, T.: A Study of Aerosol Impacts on
Clouds and Precipitation Development in a Large Winter Cyclone,
J. Atmos. Sci., 71, 3636–3658,
https://doi.org/10.1175/JAS-D-13-0305.1, 2014.
a

Aerosols can affect the evolution of deep convective clouds by controlling the cloud droplet number concentration. We perform a detailed analysis of the pathways of such aerosol perturbations through the cloud microphysics in numerical model simulations. By focussing on individually tracked convective cells, we can reveal consistent changes to individual process rates, such as a lifting of freezing and riming, but also major differences between the three different microphysics schemes used.

Aerosols can affect the evolution of deep convective clouds by controlling the cloud droplet...